Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

Aperture, A Large Telescope Using Magnetostriction For Post Deployment Corrections: Final Technical Report of NASA Innovative Advanced Concepts (NIAC) Phase I

In summary, astronomical as well as Earth observing applications of the future are counting on larger aperture telescopes than are currently available. Several groups have been working on the topic of enabling large (about 16-m diameter) UV-Vis telescopes for many years. The unique feature of our concept is that magnetic films are used rather than electrostatic films or piezo-electrostatic pads. Our magnetic film concept allows for contiguous correction along the surface, does not require a hard wire connection, and does not require continuous external application of the field. There are many unknowns related to the initial accuracy of the deployed figure prior to the magnetic write head corrections. The length scale over which the corrections need to be applied is also of concern. For, although approximately mm length scale corrections can be made with the MSM plus write head technology, the number of 1 mm patches in a 16 m diameter mirror is too large to contemplate applying individual corrections to each individual patch. However, deployment strategies and the materials available continue to evolve, in particular shape memory composites (SMCs) [34] or alloys (SMAs) [41], such that at this time we see no show-stoppers for this concept. Furthermore, the ability to tune deformations down to much (factors of 10-100) smaller (m) scale opens the futuristic possibility of improving the figure well beyond Strehl values of 90%

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

ERFVII action and modulation through oxygen-sensing in Arabidopsis thaliana

Oxygen is a key signalling component of plant biology, and whilst an oxygen-sensing mechanism was previously described in Arabidopsis thaliana, key features of the associated PLANT CYSTEINE OXIDASE (PCO) N-degron pathway and Group VII ETHYLENE RESPONSE FACTOR (ERFVII) transcription factor substrates remain untested or unknown. We demonstrate that ERFVIIs show non-autonomous activation of root hypoxia tolerance and are essential for root development and survival under oxygen limiting conditions in soil. We determine the combined effects of ERFVIIs in controlling gene expression and define genetic and environmental components required for proteasome-dependent oxygen-regulated stability of ERFVIIs through the PCO N-degron pathway. Using a plant extract, unexpected amino-terminal cysteine sulphonic acid oxidation level of ERFVIIs was observed, suggesting a requirement for additional enzymatic activity within the pathway. Our results provide a holistic understanding of the properties, functions and readouts of this oxygen-sensing mechanism defined through its role in modulating ERFVII stability

Early Neurodegeneration Progresses Independently of Microglial Activation by Heparan Sulfate in the Brain of Mucopolysaccharidosis IIIB Mice

BACKGROUND: In mucopolysaccharidosis type IIIB, a lysosomal storage disease causing early onset mental retardation in children, the production of abnormal oligosaccharidic fragments of heparan sulfate is associated with severe neuropathology and chronic brain inflammation. We addressed causative links between the biochemical, pathological and inflammatory disorders in a mouse model of this disease. METHODOLOGY/PRINCIPAL FINDINGS: In cell culture, heparan sulfate oligosaccharides activated microglial cells by signaling through the Toll-like receptor 4 and the adaptor protein MyD88. CD11b positive microglial cells and three-fold increased expression of mRNAs coding for the chemokine MIP1alpha were observed at 10 days in the brain cortex of MPSIIIB mice, but not in MPSIIIB mice deleted for the expression of Toll-like receptor 4 or the adaptor protein MyD88, indicating early priming of microglial cells by heparan sulfate oligosaccharides in the MPSIIIB mouse brain. Whereas the onset of brain inflammation was delayed for several months in doubly mutant versus MPSIIIB mice, the onset of disease markers expression was unchanged, indicating similar progression of the neurodegenerative process in the absence of microglial cell priming by heparan sulfate oligosaccharides. In contrast to younger mice, inflammation in aged MPSIIIB mice was not affected by TLR4/MyD88 deficiency. CONCLUSIONS/SIGNIFICANCE: These results indicate priming of microglia by HS oligosaccharides through the TLR4/MyD88 pathway. Although intrinsic to the disease, this phenomenon is not a major determinant of the neurodegenerative process. Inflammation may still contribute to neurodegeneration in late stages of the disease, albeit independent of TLR4/MyD88. The results support the view that neurodegeneration is primarily cell autonomous in this pediatric disease